### Preprints

Indeterminacy estimates and the size of nodal sets in singular spaces (with S. Farinelli).

*Submitted,***arXiv:2011.04409**Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications (with A. Mondino).

*Submitted,***arXiv:2004.08934**.Quantitative Obata’s Theorem (with A. Mondino and D. Semola).

*S**ubmitted*,**arXiv:1910.06637**.

### Publications

The Globalization Theorem for the Curvature Dimension Condition (with E. Milman).

**Inventiones Math.**,**arXiv:1612.07623**.Independence of synthetic Curvature Dimension conditions on transport distance exponent (with A. Akdemir, A. Colinet, R. J. McCann and F. Santarcangelo).

**Trans. Amer. Math. Soc.***,***arXiv:2007.10980****.**Displacement convexity of Entropy and the distance cost Optimal Transportation (with N. Gigli and F. Santarcangelo).

**Annales de la faculté des sciences de Toulouse***,***arXiv:2005.00243****.**New formulas for the Laplacian of distance functions and applications (with A. Mondino).

**Analysis**&**PDE**,**arXiv:1803.09687**.Isoperimetric inequality under Measure-Contraction property (with F. Santarcangelo).

**J. Funct. Anal.**, 277 (2019), 2893-2917.Quantitative isoperimetry à la Levy-Gromov (with F. Maggi and A. Mondino).

**Comm. Pure Appl. Math.**, LXXII (2019), 1631–1677.A variational time discretization for the compressible Euler equations (with M. Sedjro and M. Westdickenberg).

**Trans. Amer. Math. Soc.**, 371 (2019), 5083-5155.Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds (with A. Mondino).

**Int. Math. Res. Not.**, 2020 (2020), 1481–1510.Rigidity for critical points in the Levy-Gromov inequality (with F. Maggi and A. Mondino).

**Math. Z.**, (2018) 289: 1191.An overview of

*L*1 optimal transportation on metric measure spaces.**Measure Theory in Non-Smooth Spaces**, book chapter, edited by N. Gigli, De Gruyter Open.Optimal maps in essentially non-branching spaces (with A. Mondino).

**Commun. Contemp. Math.**, 06 (2017) 19.Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds (with A. Mondino).

**Rendiconti Lincei Matematica e Applicazioni**, Volume 29, 3 (2018) 413–430.Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds (with A. Mondino).

**Geom. Topol.**, 21 (2017) 603–645.Tangent lines and Lipschitz differentiability spaces (with T. Rajala).

**Anal. Geom. Metr. Spaces**, 4 (2016) 85–103.Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds (with A. Mondino).

**Inventiones Math.**, 208 (2017) 803–849.Measure rigidity of Ricci curvature lower bounds (with A. Mondino).

**Adv****ances****Math.**, 286 (2016) 430–480.A simple proof of global existence for the 1D Pressureless Gas Dynamics Equations (with M. Sedjro and M. Westdickenberg).

**SIAM J. Math. Anal.**, 47 (2015), no. 1, 66–79.The polar cone of the set of monotone maps (with M. Westdickenberg).

**Proc. Amer. Math. Soc.**, 143 - 2 (2015), 781–787.Decomposition of geodesics in the Wasserstein space and the globalization problem.

**Geom. Funct. Anal.**, Vol. 24 (2014) 493–551.Monge problem in metric spaces with Riemannian curvature-dimension condition.

**Nonlinear Analysis**, 99 (2014), 136–151.A note on a residual subset of Lipschitz functions on metric spaces.

**Proceedings of Edinburgh Math. Society.**, Volume 58, Issue 3, 631–636.Self-Intersection of Optimal geodesics (with M. Huesmann).

**Bull. London Math. Soc.**, 46 (2014) 653–656.Existence and uniqueness of optimal transport maps (with M. Huesmann).

**Ann. I. H. Poincare ́ AN**, 32 (2015) 1367–1377.Local Curvature-Dimension condition implies Measure-Contraction property (with K.-T. Sturm).

**J. Funct. Anal.**, 262 (2012), 5110–5127.Optimal transportation with branching distance costs and the obstacle problem.

**SIAM J. Math. Anal.**, Vol. 44 (2012), No. 1, 454–482.The Monge problem for distance cost in geodesic spaces (with S. Bianchini).

**Commun. Math. Phys.**, 318 (2013), 615–673.The Monge problem in the Wiener space.

**Calc. Var and PDE**, Vol. 45 (1-2) (2012), 101–124.

### Proceedings

The Monge problem in geodesic spaces (with S. Bianchini).

*The IMA Volumes in Mathematics and its Applications*, Vol. 153, 217–234.